In [ ]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

from sklearn import datasets
from sklearn.decomposition import PCA
from sklearn import preprocessing

sns.set() # set seaborn's default settings

First and Foremost, the dataframe has 5 basically empty rows at the top as downloaded from the source: https://www.phase-trans.msm.cam.ac.uk/map/data/materials/austenitic.data.html

(There is a naming convention for humans viewing the excel file.)

This can be fixed by using the skiprows parameter in the read_excel function.

In [ ]:
df = pd.read_excel('STMECH_AUS_SS.xls',skiprows=5) # skipping the first 5 rows of the excel file (6th row taken as column names)
df
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... Grains mm-2 Type of melting Size of ingot Product form Temperature (K) 0.2%proof_stress (M Pa) UTS (M Pa) Elongation (%) Area_reduction (%) Comments
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 298 280.000000 610.000000 67 83 NRIM/CDS/No4B/1986 ABA
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 373 243.000000 508.000000 54 83 NRIM/CDS/No4B/1986 ABA
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 473 220.000000 472.000000 44 81 NRIM/CDS/No4B/1986 ABA
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 573 204.000000 470.000000 43 76 NRIM/CDS/No4B/1986 ABA
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 673 197.000000 470.000000 45 76 NRIM/CDS/No4B/1986 ABA
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2175 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Na 2 Na 1 723 171.616375 454.047895 34.9 Na NaN
2176 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Na 2 Na 1 773 166.713050 435.415260 33 Na NaN
2177 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Na 2 Na 1 823 169.655045 424.627945 34.2 Na NaN
2178 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Na 2 Na 1 873 168.674380 398.149990 37.6 Na NaN
2179 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Na 2 Na 1 973 139.254430 296.160830 45.4 Na NaN

2180 rows × 35 columns

In [ ]:
df.index
Out[ ]:
RangeIndex(start=0, stop=2180, step=1)
In [ ]:
df.columns
Out[ ]:
Index(['Cr', 'Ni', 'Mo', 'Mn', 'Si', 'Nb', 'Ti', 'Zr', 'Ta', 'V', 'W', 'Cu',
       'N', 'C', 'B', 'P', 'S', 'Co', 'Al', 'Sn', 'Pb',
       'Solution_treatment_temperature', 'Solution_treatment_time(s)',
       'Water_Quenched_after_s.t.', 'Air_Quenched_after_s.t.', 'Grains mm-2',
       'Type of melting', 'Size of ingot', 'Product form', 'Temperature (K)',
       '0.2%proof_stress (M Pa)', 'UTS (M Pa)', 'Elongation (%)',
       'Area_reduction (%)', 'Comments'],
      dtype='object')
In [ ]:
# Lets rename the columns with easier names for our convenience
df = df.rename(columns={'Solution_treatment_temperature':'sol_temp',
                        'Solution_treatment_time(s)': 'sol_time',
                        'Water_Quenched_after_s.t.':'water_quench',
                        'Air_Quenched_after_s.t.':'air_quench',
                        'Grains mm-2':'grains',
                        'Type of melting':'melting_type',
                        'Size of ingot':'ingot_size',
                        'Product form':'product_form',
                        'Temperature (K)': 'temp',
                        '0.2%proof_stress (M Pa)': 'proof_stress',
                        'UTS (M Pa)': 'uts',
                        'Elongation (%)': 'elongation',
                        'Area_reduction (%)': 'area_reduction',
                        'Comments': 'comments'})
df.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... grains melting_type ingot_size product_form temp proof_stress uts elongation area_reduction comments
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 298 280.0 610.0 67 83 NRIM/CDS/No4B/1986 ABA
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 373 243.0 508.0 54 83 NRIM/CDS/No4B/1986 ABA
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 473 220.0 472.0 44 81 NRIM/CDS/No4B/1986 ABA
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 573 204.0 470.0 43 76 NRIM/CDS/No4B/1986 ABA
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 477.712892 1 3 1 673 197.0 470.0 45 76 NRIM/CDS/No4B/1986 ABA

5 rows × 35 columns

In [ ]:
df.shape
Out[ ]:
(2180, 35)
In [ ]:
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2180 entries, 0 to 2179
Data columns (total 35 columns):
 #   Column          Non-Null Count  Dtype  
---  ------          --------------  -----  
 0   Cr              2180 non-null   float64
 1   Ni              2180 non-null   float64
 2   Mo              2180 non-null   float64
 3   Mn              2180 non-null   float64
 4   Si              2180 non-null   float64
 5   Nb              2180 non-null   float64
 6   Ti              2180 non-null   float64
 7   Zr              2180 non-null   int64  
 8   Ta              2180 non-null   int64  
 9   V               2180 non-null   float64
 10  W               2179 non-null   float64
 11  Cu              2180 non-null   float64
 12  N               2180 non-null   float64
 13  C               2180 non-null   float64
 14  B               2180 non-null   float64
 15  P               2180 non-null   float64
 16  S               2180 non-null   float64
 17  Co              2180 non-null   float64
 18  Al              2180 non-null   float64
 19  Sn              2180 non-null   int64  
 20  Pb              2180 non-null   int64  
 21  sol_temp        2180 non-null   object 
 22  sol_time        2180 non-null   object 
 23  water_quench    2180 non-null   object 
 24  air_quench      2180 non-null   object 
 25  grains          2180 non-null   object 
 26  melting_type    2180 non-null   object 
 27  ingot_size      2180 non-null   object 
 28  product_form    2180 non-null   int64  
 29  temp            2180 non-null   int64  
 30  proof_stress    2180 non-null   float64
 31  uts             2180 non-null   float64
 32  elongation      2180 non-null   object 
 33  area_reduction  2180 non-null   object 
 34  comments        663 non-null    object 
dtypes: float64(19), int64(6), object(10)
memory usage: 596.2+ KB

We can organize our data to get two main distinct lists for categorical and numerical columns.

In [ ]:
cats = list(df.select_dtypes(include=['object']).columns)
nums = list(df.select_dtypes(exclude=['object']).columns)
print(f'categorical variables:  {cats}')
print(f'numerical variables:  {nums}')

categorical variables:  ['sol_temp', 'sol_time', 'water_quench', 'air_quench', 'grains', 'melting_type', 'ingot_size', 'elongation', 'area_reduction', 'comments']
numerical variables:  ['Cr', 'Ni', 'Mo', 'Mn', 'Si', 'Nb', 'Ti', 'Zr', 'Ta', 'V', 'W', 'Cu', 'N', 'C', 'B', 'P', 'S', 'Co', 'Al', 'Sn', 'Pb', 'product_form', 'temp', 'proof_stress', 'uts']

We can also inspect how many unique values are there in each column. This is useful to identify categorical variables that may have been misclassified as numerical due to their data type.

In [ ]:
df.nunique(axis=0)
Out[ ]:
Cr                132
Ni                145
Mo                 79
Mn                 71
Si                 54
Nb                 30
Ti                 54
Zr                  1
Ta                  1
V                  12
W                   1
Cu                 27
N                  48
C                  29
B                  27
P                  32
S                  32
Co                 18
Al                 41
Sn                  1
Pb                  1
sol_temp           20
sol_time           20
water_quench        3
air_quench          3
grains             43
melting_type        5
ingot_size         21
product_form        5
temp               20
proof_stress      371
uts               597
elongation        298
area_reduction     66
comments           60
dtype: int64

We can see from the output of our above nunquie() funciton that 5 is a value that can and should be considered categorical in this case espeically with how many rows of data we have.
Beyond 5, the next number of uniques jumps up to 20+ for non physical element columns. This is a good indicator that we should consider 5 uniques as a categorical variable.

We can then see what those 5 or less unique values are with the following:

In [ ]:
for col in df.columns:
    if df[col].nunique() <= 5:
        print(f'{col}: {df[col].unique()}')

Zr: [0]
Ta: [0]
W: [ 0. nan]
Sn: [0]
Pb: [0]
water_quench: [1 'Na' 0]
air_quench: [0 'Na' 1]
melting_type: [1 2 3 'Na' 4]
product_form: [1 2 3 4 5]

Ignoring the physical elements, we can see the that those are indeed categorical variables.

water_quench, air_quench, and melting_type, are already set as categorical in our 'cats' list, but product_form is in our numerical list, so lets fix that:
Also, elongation and sol_temp showed up as an object (probably due to Na values), but there are many unique values and they are numbers so they can be moved to numerical:

In [ ]:
cats.extend(['product_form'])
nums.remove('product_form')

nums.extend(['elongation'])
cats.remove('elongation')

nums.extend(['sol_temp'])
cats.remove('sol_temp')

print(f'categorical variables:  {cats}')
print(f'numerical variables:  {nums}')

categorical variables:  ['sol_time', 'water_quench', 'air_quench', 'grains', 'melting_type', 'ingot_size', 'area_reduction', 'comments', 'product_form']
numerical variables:  ['Cr', 'Ni', 'Mo', 'Mn', 'Si', 'Nb', 'Ti', 'Zr', 'Ta', 'V', 'W', 'Cu', 'N', 'C', 'B', 'P', 'S', 'Co', 'Al', 'Sn', 'Pb', 'temp', 'proof_stress', 'uts', 'elongation', 'sol_temp']

nans inspection¶

At this point we have noticed that some 'Na' values are appearing. From our df.info() funciton we saw non-null values for all columns.

This is because the 'Na' values are strings and not NaN values. We can fix this by replacing all 'Na' values with NaN values, and then doing some null value inspeciton and dropping rows that include them if it is a small enough part of our dataset.

In [ ]:
df = df.replace('Na', np.nan)
df.tail() # saw from earlier in the notebook the last 5 rows have 'Na' values so we can make sure they were replaced with NaN
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... grains melting_type ingot_size product_form temp proof_stress uts elongation area_reduction comments
2175 17.7 12.28 0.0 1.24 0.3 0.83 0.0 0 0 0.0 ... NaN 2.0 NaN 1 723 171.616375 454.047895 34.9 NaN NaN
2176 17.7 12.28 0.0 1.24 0.3 0.83 0.0 0 0 0.0 ... NaN 2.0 NaN 1 773 166.713050 435.415260 33.0 NaN NaN
2177 17.7 12.28 0.0 1.24 0.3 0.83 0.0 0 0 0.0 ... NaN 2.0 NaN 1 823 169.655045 424.627945 34.2 NaN NaN
2178 17.7 12.28 0.0 1.24 0.3 0.83 0.0 0 0 0.0 ... NaN 2.0 NaN 1 873 168.674380 398.149990 37.6 NaN NaN
2179 17.7 12.28 0.0 1.24 0.3 0.83 0.0 0 0 0.0 ... NaN 2.0 NaN 1 973 139.254430 296.160830 45.4 NaN NaN

5 rows × 35 columns

In [ ]:
df.isnull().any()
Out[ ]:
Cr                False
Ni                False
Mo                False
Mn                False
Si                False
Nb                False
Ti                False
Zr                False
Ta                False
V                 False
W                  True
Cu                False
N                 False
C                 False
B                 False
P                 False
S                 False
Co                False
Al                False
Sn                False
Pb                False
sol_temp           True
sol_time           True
water_quench       True
air_quench         True
grains             True
melting_type       True
ingot_size         True
product_form      False
temp              False
proof_stress      False
uts               False
elongation         True
area_reduction     True
comments           True
dtype: bool
In [ ]:
df.isna().sum()
Out[ ]:
Cr                   0
Ni                   0
Mo                   0
Mn                   0
Si                   0
Nb                   0
Ti                   0
Zr                   0
Ta                   0
V                    0
W                    1
Cu                   0
N                    0
C                    0
B                    0
P                    0
S                    0
Co                   0
Al                   0
Sn                   0
Pb                   0
sol_temp           184
sol_time          1097
water_quench       264
air_quench         264
grains            1517
melting_type       217
ingot_size        1517
product_form         0
temp                 0
proof_stress         0
uts                  0
elongation          95
area_reduction    1517
comments          1517
dtype: int64
In [ ]:
df.isna().sum().sum()
Out[ ]:
8190
In [ ]:
df.shape
Out[ ]:
(2180, 35)
In [ ]:
# nan proportion in data
8190 / len(df) #this is single NaN values compared to the total number of rows
Out[ ]:
3.756880733944954

We have too many rows to drop all rows with NaN values, so we will drop rows with NaN values in the following columns:

In [ ]:
# Checking if null values are from the same rows for large null value columns
columns_with_many_nulls = df.isna().sum() > 200
selected_columns = df.columns[columns_with_many_nulls]
df_nulls = df[selected_columns]
df_nulls.isna().sum()
Out[ ]:
sol_time          1097
water_quench       264
air_quench         264
grains            1517
melting_type       217
ingot_size        1517
area_reduction    1517
comments          1517
dtype: int64
In [ ]:
null_rows = df_nulls.isnull().all(axis=1)
null_rows.sum()
Out[ ]:
3

This shows only 3 rows there there are full NaN rows. We can drop those for sure, but there are way too many other NaN values that should be dropped.
Lets do that again but increase the columns_with_many_nulls parameter to look for > 300, not just 200:

In [ ]:
# Checking if null values are from the same rows for large null value columns
columns_with_many_nulls = df.isna().sum() > 300
selected_columns = df.columns[columns_with_many_nulls]
df_nulls = df[selected_columns]
df_nulls.isna().sum()
Out[ ]:
sol_time          1097
grains            1517
ingot_size        1517
area_reduction    1517
comments          1517
dtype: int64
In [ ]:
null_rows = df_nulls.isnull().all(axis=1)
null_rows.sum()
Out[ ]:
800

We can see now that we have 800 rows that are fully NaN on these columns. We can drop those rows:

In [ ]:
df.shape
Out[ ]:
(2180, 35)
In [ ]:
df_firstdrop = df.loc[~null_rows]
df_firstdrop.shape
Out[ ]:
(1380, 35)

We can see from our two df.shape command that those 800 all null value rows (for selected columns) have been dropped from the dataframe.

At this point, we could do other methods to only drop rows if the NaN value is in certian columns, or we can just drop all columns with NaN values and come back to our df_firstdrop dataframe if we want to do more analysis on/around the NaN values later.

In [ ]:
df_firstdrop = df_firstdrop.dropna(axis=0)
df_firstdrop.shape
Out[ ]:
(365, 35)
In [ ]:
365/2180
Out[ ]:
0.16743119266055045

So, if we did that, we would only be keeping 16.7% of the inital data set. This may be an okay amount of data to work with but we are not sure until we do some more analysis.

Another method would be to drop all columns with a large amount NaN values, and then finish with dropping rows with NaN values. This would be a good method if we wanted to keep more of the data but less features/columns. In this case, we think proof_stress, uts, and elongation are the going to be the results we are looking for / the output of our model, and all the physical elements as well as solution tretment temp as inputs. There may be more inputs, but those from inital inspection seem like the most important. Those columns don't have a lot of NaN values like some other columsns. Thus, we will first drop those columns with a lot of NaN values, and then drop rows with NaN values to preserve as much data in columns we care about.

So, lets drop all columns with > 300 NaN values:

In [ ]:
columns_to_drop = columns_with_many_nulls[columns_with_many_nulls].index
columns_to_drop
Out[ ]:
Index(['sol_time', 'grains', 'ingot_size', 'area_reduction', 'comments'], dtype='object')
In [ ]:
df2 = df.drop(columns_to_drop, axis=1)
df2.shape
Out[ ]:
(2180, 30)
In [ ]:
df2.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... Pb sol_temp water_quench air_quench melting_type product_form temp proof_stress uts elongation
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0 1403.0 1.0 0.0 1.0 1 298 280.0 610.0 67.0
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0 1403.0 1.0 0.0 1.0 1 373 243.0 508.0 54.0
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0 1403.0 1.0 0.0 1.0 1 473 220.0 472.0 44.0
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0 1403.0 1.0 0.0 1.0 1 573 204.0 470.0 43.0
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0 1403.0 1.0 0.0 1.0 1 673 197.0 470.0 45.0

5 rows × 30 columns

In [ ]:
df2.isna().sum()
Out[ ]:
Cr                0
Ni                0
Mo                0
Mn                0
Si                0
Nb                0
Ti                0
Zr                0
Ta                0
V                 0
W                 1
Cu                0
N                 0
C                 0
B                 0
P                 0
S                 0
Co                0
Al                0
Sn                0
Pb                0
sol_temp        184
water_quench    264
air_quench      264
melting_type    217
product_form      0
temp              0
proof_stress      0
uts               0
elongation       95
dtype: int64
In [ ]:
df2.isna().sum().sum()
Out[ ]:
1025
In [ ]:
df2 = df2.dropna(axis=0)
df2.shape
Out[ ]:
(1635, 30)
In [ ]:
df2.reset_index(drop=True, inplace=True) #reindexing the dataframe
In [ ]:
columns_with_many_nulls
Out[ ]:
Cr                False
Ni                False
Mo                False
Mn                False
Si                False
Nb                False
Ti                False
Zr                False
Ta                False
V                 False
W                 False
Cu                False
N                 False
C                 False
B                 False
P                 False
S                 False
Co                False
Al                False
Sn                False
Pb                False
sol_temp          False
sol_time           True
water_quench      False
air_quench        False
grains             True
melting_type      False
ingot_size         True
product_form      False
temp              False
proof_stress      False
uts               False
elongation        False
area_reduction     True
comments           True
dtype: bool
In [ ]:
cats
Out[ ]:
['sol_time',
 'water_quench',
 'air_quench',
 'grains',
 'melting_type',
 'ingot_size',
 'area_reduction',
 'comments',
 'product_form']
In [ ]:
cats = [cat for cat in cats if not columns_with_many_nulls[cat]] # updats cats to remove columns with many nulls
cats
Out[ ]:
['water_quench', 'air_quench', 'melting_type', 'product_form']

None of the columns we dropped are numerical so we do not have to update our nums list.

In [ ]:
print(df.shape)
print(df2.shape)

(2180, 35)
(1635, 30)
In [ ]:
df2.shape[0]/df.shape[0]
Out[ ]:
0.75

Keeping 75% of the rows of our inital data set is much better than the 16.7% we had previously.
(As long as we don't need any of the 5 columns we dropped; If we do in the future, we can come back to it.)

Check for duplicates

In [ ]:
df.duplicated().sum()
Out[ ]:
0

Encoding¶

We can convert some categorical columns that have intergers to strings for easier human readability:

In [ ]:
for col in df2.columns:
    if col in cats: # if the column is categorical
        if df2[col].nunique() <= 5:
            print(f'{col}: {df2[col].unique()}')

water_quench: [1. 0.]
air_quench: [0. 1.]
melting_type: [1. 2. 3. 4.]
product_form: [1 2 3 4 5]
In [ ]:
# Melting Type:
# 1 = BEA (basic electric arc furnace)
# 2 = HFIF (high frequency induction furnace)
# 3 = EF (electric furnace)
# 4 = Unsure        # dataset does not state what the 5th value is

df2['melting_type_name'] = df['melting_type'].map({1: 'BEA', 2: 'HFIF', 3: 'EF', 4: 'Unsure'}) # add a column easier human user readability

# Product Form:
# 1 = Tube
# 2 = Plate
# 3 = Bar
# 4 = Bloom
# 5 = Unsure        # dataset does not state what the 5th value is

df2['product_form_name'] = df['product_form'].map({1: 'Tube', 2: 'Plate', 3: 'Bar', 4: 'Bloom', 5: 'Unsure'}) # add a column for easier human user readability

df2.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... water_quench air_quench melting_type product_form temp proof_stress uts elongation melting_type_name product_form_name
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 1.0 0.0 1.0 1 298 280.0 610.0 67.0 BEA Tube
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 1.0 0.0 1.0 1 373 243.0 508.0 54.0 BEA Tube
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 1.0 0.0 1.0 1 473 220.0 472.0 44.0 BEA Tube
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 1.0 0.0 1.0 1 573 204.0 470.0 43.0 BEA Tube
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 1.0 0.0 1.0 1 673 197.0 470.0 45.0 BEA Tube

5 rows × 32 columns

water_quench and air_quench's 1 and 0 values we can assume are True and False respectively so we can convert those to bools (not necessary)

In [ ]:
df2['water_quench'] = df2['water_quench'].apply(lambda x: True if x == 1 else False)
df2['air_quench'] = df2['air_quench'].apply(lambda x: True if x == 1 else False)

df2.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... water_quench air_quench melting_type product_form temp proof_stress uts elongation melting_type_name product_form_name
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... True False 1.0 1 298 280.0 610.0 67.0 BEA Tube
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... True False 1.0 1 373 243.0 508.0 54.0 BEA Tube
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... True False 1.0 1 473 220.0 472.0 44.0 BEA Tube
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... True False 1.0 1 573 204.0 470.0 43.0 BEA Tube
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... True False 1.0 1 673 197.0 470.0 45.0 BEA Tube

5 rows × 32 columns

Then, we can encode these categorical columns to get boolean columns that can be useful for our model later. (1 column for each unique value for each categorical column.)

In [ ]:
ohe = preprocessing.OneHotEncoder(sparse_output=False)

melting_ohe = ohe.fit_transform(df2[['melting_type']])
product_form_ohe = ohe.fit_transform(df2[['product_form']])

df2['melting_ohe_1'] = melting_ohe[:,0]
df2['melting_ohe_2'] = melting_ohe[:,1]
df2['melting_ohe_3'] = melting_ohe[:,2]
df2['melting_ohe_4'] = melting_ohe[:,3]


df2['product_form_1'] = product_form_ohe[:,0]
df2['product_form_2'] = product_form_ohe[:,1]
df2['product_form_3'] = product_form_ohe[:,2]
df2['product_form_4'] = product_form_ohe[:,3]
df2['product_form_5'] = product_form_ohe[:,4]

df2
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... product_form_name melting_ohe_1 melting_ohe_2 melting_ohe_3 melting_ohe_4 product_form_1 product_form_2 product_form_3 product_form_4 product_form_5
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... Tube 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... Tube 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... Tube 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... Tube 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... Tube 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
1630 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Unsure 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
1631 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Unsure 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
1632 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Tube 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
1633 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Tube 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
1634 17.7 12.28 0.00 1.24 0.30 0.83 0.00 0 0 0.0 ... Tube 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0

1635 rows × 41 columns

These encoding columns can also be converted to bools but we can leave it for now.

Recap of our current dataframe using info() and describe():

In [ ]:
df2.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1635 entries, 0 to 1634
Data columns (total 41 columns):
 #   Column             Non-Null Count  Dtype  
---  ------             --------------  -----  
 0   Cr                 1635 non-null   float64
 1   Ni                 1635 non-null   float64
 2   Mo                 1635 non-null   float64
 3   Mn                 1635 non-null   float64
 4   Si                 1635 non-null   float64
 5   Nb                 1635 non-null   float64
 6   Ti                 1635 non-null   float64
 7   Zr                 1635 non-null   int64  
 8   Ta                 1635 non-null   int64  
 9   V                  1635 non-null   float64
 10  W                  1635 non-null   float64
 11  Cu                 1635 non-null   float64
 12  N                  1635 non-null   float64
 13  C                  1635 non-null   float64
 14  B                  1635 non-null   float64
 15  P                  1635 non-null   float64
 16  S                  1635 non-null   float64
 17  Co                 1635 non-null   float64
 18  Al                 1635 non-null   float64
 19  Sn                 1635 non-null   int64  
 20  Pb                 1635 non-null   int64  
 21  sol_temp           1635 non-null   float64
 22  water_quench       1635 non-null   bool   
 23  air_quench         1635 non-null   bool   
 24  melting_type       1635 non-null   float64
 25  product_form       1635 non-null   int64  
 26  temp               1635 non-null   int64  
 27  proof_stress       1635 non-null   float64
 28  uts                1635 non-null   float64
 29  elongation         1635 non-null   float64
 30  melting_type_name  1500 non-null   object 
 31  product_form_name  1635 non-null   object 
 32  melting_ohe_1      1635 non-null   float64
 33  melting_ohe_2      1635 non-null   float64
 34  melting_ohe_3      1635 non-null   float64
 35  melting_ohe_4      1635 non-null   float64
 36  product_form_1     1635 non-null   float64
 37  product_form_2     1635 non-null   float64
 38  product_form_3     1635 non-null   float64
 39  product_form_4     1635 non-null   float64
 40  product_form_5     1635 non-null   float64
dtypes: bool(2), float64(31), int64(6), object(2)
memory usage: 501.5+ KB
In [ ]:
df2.describe()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... elongation melting_ohe_1 melting_ohe_2 melting_ohe_3 melting_ohe_4 product_form_1 product_form_2 product_form_3 product_form_4 product_form_5
count 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.0 1635.0 1635.000000 ... 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000 1635.000000
mean 17.815523 12.616716 1.037889 1.471456 0.500153 0.088600 0.140623 0.0 0.0 0.002716 ... 46.775413 0.651376 0.240367 0.026300 0.081957 0.763914 0.108257 0.113761 0.004893 0.009174
std 0.997062 5.149107 1.173163 0.234563 0.129131 0.250785 0.202740 0.0 0.0 0.010523 ... 19.069181 0.476680 0.427437 0.160074 0.274383 0.424805 0.310800 0.317618 0.069800 0.095371
min 15.900000 8.400000 0.000000 0.610000 0.000000 0.000000 0.000000 0.0 0.0 0.000000 ... 11.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
25% 17.105000 10.440000 0.000000 1.430000 0.400000 0.000000 0.000000 0.0 0.0 0.000000 ... 39.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000
50% 17.690000 11.650000 0.120000 1.520000 0.490000 0.000000 0.011000 0.0 0.0 0.000000 ... 44.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000
75% 18.200000 12.240000 2.390000 1.620000 0.580000 0.010000 0.390000 0.0 0.0 0.000000 ... 50.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000
max 21.060000 34.450000 2.910000 1.820000 0.820000 0.950000 0.560000 0.0 0.0 0.057000 ... 505.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

8 rows × 37 columns

Normalization¶

In [ ]:
mx = '_mxm'
nums_mxm = []
for s in nums:
    s = s + mx
    nums_mxm.append(s)
print(nums_mxm)

['Cr_mxm', 'Ni_mxm', 'Mo_mxm', 'Mn_mxm', 'Si_mxm', 'Nb_mxm', 'Ti_mxm', 'Zr_mxm', 'Ta_mxm', 'V_mxm', 'W_mxm', 'Cu_mxm', 'N_mxm', 'C_mxm', 'B_mxm', 'P_mxm', 'S_mxm', 'Co_mxm', 'Al_mxm', 'Sn_mxm', 'Pb_mxm', 'temp_mxm', 'proof_stress_mxm', 'uts_mxm', 'elongation_mxm', 'sol_temp_mxm']
In [ ]:
mxm_Scaler = preprocessing.MinMaxScaler()

mxm_Scaler.fit(df2[nums])

df2[nums_mxm] = mxm_Scaler.transform(df2[nums])
df2.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... S_mxm Co_mxm Al_mxm Sn_mxm Pb_mxm temp_mxm proof_stress_mxm uts_mxm elongation_mxm sol_temp_mxm
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0.26 0.0 0.090385 0.0 0.0 0.005102 0.799944 0.844174 0.113360 0.611111
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0.26 0.0 0.090385 0.0 0.0 0.081633 0.679136 0.691233 0.087045 0.611111
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0.26 0.0 0.090385 0.0 0.0 0.183673 0.604039 0.637254 0.066802 0.611111
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0.26 0.0 0.090385 0.0 0.0 0.285714 0.551798 0.634255 0.064777 0.611111
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... 0.26 0.0 0.090385 0.0 0.0 0.387755 0.528943 0.634255 0.068826 0.611111

5 rows × 67 columns

We can see below a historgram showing that column has been normalized.

In [ ]:
fig1, ax1 = plt.subplots(1,2, figsize=(9,5))

df2['temp'].plot(kind='hist', ax=ax1[0], color='r')
df2['temp_mxm'].plot(kind='hist', ax=ax1[1], color='g')
Out[ ]:
<Axes: ylabel='Frequency'>
In [ ]:
print(df2['temp_mxm'].min())
print(df2['temp_mxm'].max())

0.0
1.0

min and max shown

Standardization¶

In [ ]:
sc = '_std'
nums_std = []
for s in nums:
    s = s + sc
    nums_std.append(s)
print(nums_std)

['Cr_std', 'Ni_std', 'Mo_std', 'Mn_std', 'Si_std', 'Nb_std', 'Ti_std', 'Zr_std', 'Ta_std', 'V_std', 'W_std', 'Cu_std', 'N_std', 'C_std', 'B_std', 'P_std', 'S_std', 'Co_std', 'Al_std', 'Sn_std', 'Pb_std', 'temp_std', 'proof_stress_std', 'uts_std', 'elongation_std', 'sol_temp_std']
In [ ]:
std_Scaler = preprocessing.StandardScaler()

std_Scaler.fit(df2[nums])

df2[nums_std] = std_Scaler.transform(df2[nums])
df2.head()
Out[ ]:
Cr Ni Mo Mn Si Nb Ti Zr Ta V ... S_std Co_std Al_std Sn_std Pb_std temp_std proof_stress_std uts_std elongation_std sol_temp_std
0 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... -0.07496 -0.347715 0.119597 0.0 0.0 -1.620783 2.644018 1.867801 1.060915 1.068692
1 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... -0.07496 -0.347715 0.119597 0.0 0.0 -1.298939 1.848761 0.789396 0.378978 1.068692
2 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... -0.07496 -0.347715 0.119597 0.0 0.0 -0.869813 1.354413 0.408783 -0.145589 1.068692
3 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... -0.07496 -0.347715 0.119597 0.0 0.0 -0.440687 1.010518 0.387638 -0.198046 1.068692
4 18.7 10.69 0.47 1.56 0.62 0.01 0.04 0 0 0.0 ... -0.07496 -0.347715 0.119597 0.0 0.0 -0.011561 0.860064 0.387638 -0.093132 1.068692

5 rows × 93 columns

In [ ]:
fig2, ax2 = plt.subplots(1,2, figsize=(9,5))

df2['temp'].plot(kind='hist', ax=ax2[0], color='r')
df2['temp_std'].plot(kind='hist', ax=ax2[1], color='g')
Out[ ]:
<Axes: ylabel='Frequency'>
In [ ]:
df2.temp_std.describe()
Out[ ]:
count    1.635000e+03
mean    -1.042999e-16
std      1.000306e+00
min     -1.642239e+00
25%     -8.698129e-01
50%     -1.156146e-02
75%      8.466900e-01
max      2.563193e+00
Name: temp_std, dtype: float64

standard deviation 'std' of ~1 shown

Visualization¶

Now that our data is cleaned and prepared, we can move on to visualizing it.

Recap of our categorical and numerical columns:

In [ ]:
cats
Out[ ]:
['water_quench', 'air_quench', 'melting_type', 'product_form']
In [ ]:
nums
Out[ ]:
['Cr',
 'Ni',
 'Mo',
 'Mn',
 'Si',
 'Nb',
 'Ti',
 'Zr',
 'Ta',
 'V',
 'W',
 'Cu',
 'N',
 'C',
 'B',
 'P',
 'S',
 'Co',
 'Al',
 'Sn',
 'Pb',
 'temp',
 'proof_stress',
 'uts',
 'elongation',
 'sol_temp']
In [ ]:
fig, ax3 = plt.subplots()

scatter_plot = ax3.scatter(x=df2.temp_mxm, y=df2.uts_mxm, s=df2.elongation_mxm*200, c=df2.proof_stress_mxm) # s scaled for better visuals

cbar = plt.colorbar(scatter_plot)
cbar.set_label('proof_stress')
ax3.set_xlabel('temp')
ax3.set_ylabel('uts')
plt.show()

This preliminary plot shows a correlation between temperature, ultimate tensile strength, and proof stress.
As temperature increases, ultimate tensile strength and proof stress decrease; elongation increases slightly.

Another observation was how outliers can easily be seen in the data.

Making Plots With Hue of Categorical Columns Looking for Clusters

In [ ]:
sns.pairplot(df2, vars=df2.loc[:, nums[0:21]].columns, hue='product_form_name')  # This is a lot of data to plot, so it takes a while (4-5 min) to load
plt.show()

This inital pairplot has too much data to analyze like this, but we can look at some lines shown to see what physical elements might be good to focus on.

In [ ]:
sns.pairplot(df2, vars=df2.loc[:, nums_mxm[21:25]].columns, hue='product_form_name')
plt.show()
In [ ]:
sns.pairplot(df2, vars=df2.loc[:, nums_mxm[21:25]].columns, hue='melting_type_name')
plt.show()
In [ ]:
df2['quench_type_name'] = df2['water_quench'].apply(lambda x: 'water' if x else 'air') # add a column for easier human user readability and plotting

sns.pairplot(df2, vars=df2.loc[:, nums_mxm[21:25]].columns, hue='quench_type_name')
plt.show()

From the three smaller size / normal looking pair plots just shown, it can bee seen that Tube and BEA have high correlation while other product forms and meltling types do not have as much correlation.
Also, water quenching definetly decreases the phyiscal properties of the material.

Additionally, the outliers are messing up the data. If the outliers were removed, we might see more correlation in the plots.

In [ ]:
sns.countplot(data=df2, x='product_form_name')
Out[ ]:
<Axes: xlabel='product_form_name', ylabel='count'>
In [ ]:
sns.countplot(data=df2, x='melting_type_name')
Out[ ]:
<Axes: xlabel='melting_type_name', ylabel='count'>

Now we can see that 'Tube' and 'BEA' were the most highly correlated because of the amount of data points they had, not because of real world condtions. We may want to use these two types if we were to look at other correlations in the data.

In [ ]:
sns.countplot(data=df2, x='quench_type_name')
Out[ ]:
<Axes: xlabel='quench_type_name', ylabel='count'>
In [ ]:
hm1 = sns.heatmap(df2[nums[21:25]].corr(), annot=True)

It can be seen that ultlimate tensile strength and proof stress are highly correlated, and elongation is not as correlated to other physical properties.

We can also lookat

In [ ]:
fig, ax4 = plt.subplots()

scatter_plot = ax4.scatter(x=df2.Nb_mxm, y=df2.proof_stress_mxm, s=df2.elongation_mxm*200, c=df2.uts_mxm) # s scaled for better visuals

cbar = plt.colorbar(scatter_plot)
cbar.set_label('uts')
ax4.set_xlabel('Nb')
ax4.set_ylabel('proof_stress')
plt.show()

We can see that for the alloys, the more Niobium in it, the there is generally more stable proof stress and ultimate tensile strength. This can just be due to lower amount of data points at the higher end of Niobium though, and each element must be looked at to ensure accurate conclusions.

In [ ]:
sns.boxplot(data=df2, x='melting_type_name', y='proof_stress_mxm')
Out[ ]:
<Axes: xlabel='melting_type_name', ylabel='proof_stress_mxm'>

One more thing that we were just able to see with this box plot is that the 'EF' melting type has a more closely distributed proof stress than the other melting types. This could be indicative that EF is a more consistent melting type than the others.